Difference between revisions of "2017 AMC 10A Problems/Problem 22"
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Sides <math>\overline{AB}</math> and <math>\overline{AC}</math> of equilateral triangle <math>ABC</math> are tangent to a circle as points <math>B</math> and <math>C</math> respectively. What fraction of the area of <math>\triangle ABC</math> lies outside the circle? | Sides <math>\overline{AB}</math> and <math>\overline{AC}</math> of equilateral triangle <math>ABC</math> are tangent to a circle as points <math>B</math> and <math>C</math> respectively. What fraction of the area of <math>\triangle ABC</math> lies outside the circle? | ||
<math> \mathrm{(A) \ }\dfrac{4\sqrt{3}\pi}{27}-\frac{1}{3}\qquad \mathrm{(B) \ } \frac{\sqrt{3}}{2}-\frac{\pi}{8}\qquad \mathrm{(C) \ } \frac{1}{2} \qquad \mathrm{(D) \ }\sqrt{3}-\frac{2\sqrt{3}\pi}{9}\qquad \mathrm{(E) \ } \frac{4}{3}-\dfrac{4\sqrt{3}\pi}{27}</math> | <math> \mathrm{(A) \ }\dfrac{4\sqrt{3}\pi}{27}-\frac{1}{3}\qquad \mathrm{(B) \ } \frac{\sqrt{3}}{2}-\frac{\pi}{8}\qquad \mathrm{(C) \ } \frac{1}{2} \qquad \mathrm{(D) \ }\sqrt{3}-\frac{2\sqrt{3}\pi}{9}\qquad \mathrm{(E) \ } \frac{4}{3}-\dfrac{4\sqrt{3}\pi}{27}</math> | ||
Revision as of 16:26, 8 February 2017
Problem
Sides 
and 
of equilateral triangle 
are tangent to a circle as points 
and 
respectively. What fraction of the area of 
lies outside the circle?
